Applied mathematics

This Lecture Note deals with asymptotic properties, i.

The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field.

3D CAD is one of the most important technologies of the 90sfor the engineering and manufacturing world.

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space.

Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives.

Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years.

Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world.

Risk management for financial institutions is one of the key topics the financial industry has to deal with.

Asymptotic analysis of stochastic stock price models is the central topic of the present volume.

This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator.

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces.

The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up.

This richly illustrated book is an exploration of how chance and risk, on the one hand, and meaning or significance on the other, compete for the limelight in art, in philosophy, and in science.

In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications.

Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance.

It was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?

Quantum trajectory theory is largely employed in theoretical quantum optics and quantum open system theory and is closely related to the conceptual formalism of quantum mechanics (quantum measurement theory).

This book is about synergy in computational intelligence (CI).

This book addresses the applications of Fourier transform to smile modeling.

Thereareabout500booksonvariationalprinciples.

The aim of publishing this book is the further development of the concept of dissipative solitons, which has been in the air for at least the last decade and a half.

For this printing of R.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics.

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology.

Stochastic control theory is a relatively young branch of mathematics.

In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling.

Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of  financial derivatives and structured products in the financial markets around the globe and the surge in research on derivative pricing theory.

Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions.

Introduction This book presents and develops major numerical methods currently used for solving problems arising in quantitative ?

This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists.

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory.

The book concerns limit theorems and laws of large numbersfor scaled unionsof independent identically distributedrandom sets.

This volume represents a part of the main result obtained bya group of French probabilists, together with thecontributions of a number of colleagues, mainly from the USAand Japan.

In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes.

White Noise Calculus is a distribution theory on Gaussian space, proposed by T.

The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research.

This book is composed of two texts, by R.

These proceedings of the fifth joint meeting of Japanese and Soviet probabilists are a sequel to Lecture Notes in Mathematics Vols.

The theory of Dirichlet forms has witnessed recently somevery important developments both in theoretical foundationsand in applications (stochasticprocesses, quantum fieldtheory, composite materials,.

This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St.

In this volume of original research papers, the main topics discussed relate to the asymptotic windings of planar Brownian motion, structure equations, closure properties of stochastic integrals.

1) Phase Transitions, represented by generalizations of the classical Stefan problem.

This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field.

The number field sieve is an algorithm for finding the prime factors of large integers.

In recent years products based on ?

This second BiBoS volume surveys recent developments in the theory of stochastic processes.